David,
the flare problem would be much less than in a round less, simply because there would be much less lens.
(To be precise, one should take into acount that one would use slit light shade with a classical panoramic camera and thus reduce flare too.)
Mustafa,
I have to correct myself (again you had a thoughtprovoking idea...):
There would not be an aperture (speed) problem of that slice lens. As there only is a slice to be exposed at a time there is only a slice of aperture needed.
I thought of another obstacle, namely diffraction which would be induced be a very small slit mask (needed to form that slice).
However,
-) when using film one could make a slit mask that actually lies on the film. Then there would be no space into which light could be diffracted.
-) when using an electronic sensor of the CCD type or so one would not need a slit mask at all.
In case of a swing (slice) lens type of panoramic camera one could arrange the seperate lines of the sensor in parallel to the plane of the slit lens (or rather the virtual slit) Then one only would need to readout the very lines line after line while the small strip of light passes them. No mask would be needed as only a single line is read at a time. (Well, the sensor plane must of course be bent; something very impractible...)
In case of a rotating type of panoramic camera only a single-line sensor must be used, which is read out repeatedly while the camera rotates.